Heat Flux for a Relativistic Dilute Bidimensional Gas

Abstract

Relativistic kinetic theory predicts substantial modifications to the dissipation mechanisms of a dilute gas. For the heat flux, these include (in the absence of external forces) a correction to the thermal conductivity and the appearance of a new, purely relativistic, term proportional to the density gradient. In this work we obtain such constitutive equation for the particular case of a bidimensional gas. The calculation is based on the Chapman–Enskog solution to the relativistic Boltzmann equation and yields analytical expressions for the corresponding transport coefficients, which are evaluated for the particular case of hard disks. These results will be useful for numerical simulations and may be applied to bidimensional non-dense materials.

and choosing the center of mass frame where the spatial components of \(P^{\nu }\) vanish and assuming, without loss of generality, that the \(x_{2}\) axis is in the direction of \(Q^{\alpha }\) such that